Davidson College student, Jane Gribble, was our March Mathness winner this year. Below she explains how she filled in her bracket.

I love basketball – Davidson College basketball. As a Davidson College cheerleader I have an enormous amount of school pride, especially when it comes to our basketball team. However, outside of Davidson College I know little to nothing about college basketball. I knew that UNC Chapel Hill was having a tough season because this is my sister’s alma mater. Also, I knew that New Mexico, Gonzaga, Duke, and Montana were all likely teams for the NCAA tournament because we had played these non-conference teams during our season and these were the most talked about non-conference games around campus. My name is Jane Gribble. I am a junior mathematics major and this is the first year I completed a bracket.

In Dr. Tim Chartier’s MAT 210 – Mathematical Modeling course we discussed sports ranking using the Colley method and the Massey method. We were given the opportunity to apply our new knowledge of sports ranking in the NCAA Tournament Challenge. Since Davidson College was participating in the tournament my focus was on one game, the Davidson/Marquette game in Lexington, KY. When we traveled to KY I thought I had missed my opportunity to fill out a bracket, but one of my classmates was also traveling for the game with the Davidson College Pep Band and had the modeling program on his computer. We completed our brackets in the hotel lobby in Kentucky the night before our game.

My bracket used the Massey method because in previous years it has had better success than the Colley method. I decided to submit only one bracket, a bracket solely based on math (partially because I know little about college basketball). As a cheerleader and a prideful student it upset me to have Davidson losing against Marquette the following night, but I wasn’t going to let a math model crush my personal dreams of success in the tournament. The home games were weighted as .5 (it would have been 1 if it was an unweighted model) to take into account home court advantage. Similarly, away games were weighted as 1.5 and neutral games as 1. Also, the season was segmented into 6 equal sections. I believe games at the end of the season are more important than games at the beginning of the season because teams change throughout the year and the last games give the best perspective of the teams going into the tournament. There was no real reason for the numbers chosen, other than they increased each segment. The 6 equal sections were weighted: .4, .6, .8, 1, 1.5, and 2. With these weights in the Massey method my model correctly predicted the Minnesota upset, but missed the Ole Miss, LaSalle, Harvard, and Florida Gulf upsets.

After Davidson’s tragic loss I could not watch anymore basketball for a while. I even forgot that my bracket was in the competition. I only started paying attention to the brackets when a friend in the same competition congratulated me on being second going into the Elite 8; my math based bracket was in the top 10 percent of all the brackets. Once he told me my bracket had a chance of winning, I paid attention to the rest of the games to see how my bracket was doing in the competition. After Davidson’s loss against Louisville last year in the tournament I never wanted to cheer for Louisville. To my surprise, I went into the final game this year cheering for Louisville because my model had Louisville winning it all. I was not cheering for Louisville because of any connections with the team, but was cheering to receive a free ice cream cone, a prize that our local Ben and Jerry’s donates to the winner of Dr. Chartier’s class pool.

Next year I hope to compete in the NCAA tournament challenge again. This year I greatly enjoyed the experience and want to continuing submitting brackets for the tournament. Next year I will submit one bracket that uses the exact weightings of my bracket this year to see how it compares from year to year. This year I wanted to submit a math bracket that looked at teams who had injuries throughout the season. My motivation for this was Davidson’s player Clint Mann. Clint had to sit out many games towards the end of the season because of a concussion, but he had recovered in time for the NCAA tournament. I thought that our wins during the time without Clint showed our strengths as a team. Unfortunately this year I ran out of time to code this additional weighting. Hopefully next year my submissions will include a bracket using the weights from this year, a bracket that includes weights for teams with injured team members, and another bracket with varying weights.

John Hussey and Vickie Kearn both work at Princeton University Press. John is the assistant sales director and national accounts manager and Vickie is the mathematics editor. We thought it would be fun to see how they filled out their March Madness brackets. The conversation that follows took place on March 20 at our PUP offices. To get things started, we asked a single question: How did you fill out your bracket?

Vickie: You may have figured out I am the math geek. After getting my math degree at the University of Richmond, I taught math for 8 years and then ventured into publishing math books. Although I am a huge sports fan, my true love is football. I didn’t watch basketball until we began March Mathness a couple of years ago. Now I will be glued to the TV for the next few weeks. I really don’t know much about the game at all but I love watching the numbers and the great upsets, especially those we have seen so far this year.

Now to my bracket. Because of the many upsets this year, I decided to ignore the seeds.

I looked at four things when I filled in my bracket:

1. Strength of schedule (pulled from RPI). I gave this figure a weight of 1.
2. Winning percentage for the regular season earned a weight of 1.
3. The sum of the posts season wins over the past three years plus the coach’s winning record with their current team also got a weight of 1.
4. Then each team received the following bonus points.

-One point if they were the leader in their conference in the regular season.
-One point if they are a major team and if they are in a tested basketball conference like the ACC, Big East, and Big10.
-One point if they won their conference championship season
-One point for the leaders in points per game/rebounds per game/scoring offense and scoring defense

Bonus points are weighted as 2 because they reflect how the teams were playing at the end of the season.

John: What about style of play?

Vickie: I don’t know that much about basketball, I’m in March Madness for the math. I’m interested in the data and stats.

John: To get an understanding of my approach, here’s my background: I went to Syracuse University for sports broadcasting. I have friends that still work in sports. My picks are based on a personal study of the game; I watch about 20 hours of sports/week and college basketball is my favorite. My picks are similar to Vickie’s, but from a different point of view. I’m not distinguishing between conference tournament and how a team plays through the stretch of the season. I’ve been watching teams play and deciding on style of play. For example, if one team tends to make a lot of 3-pointers and they’re up against a team with a strong zone defense, the zone defense is not going to do well. Where things get tricky is making decisions about Syracuse. Since that’s my team I’m pretty biased. When you watch teams extensively, you have seen them in the good times and bad but the bad times stick in your mind. For example, Kansas’ loss at TCU or Michigan’s loss at Penn State. I also know a lot about upset histories. This year there are no #1 seeds in my final bracket because this year no one team dominated. The possibilities are wider this year…could be a five seed that wins.

Vickie: I only have one #1 seed in my final 4. We both picked #2 seed Duke as the 2013 champion.

John: Player experience is also a big factor. Some game style doesn’t translate into a tournament setting. Duke is a great team, but sometimes flakes out super early. They lost to Lehigh last year but they make lot of deep runs. It’s interesting that Miami is in Vickie’s final 4 but I have them flaming out in the 2nd round. They’re too reliant on 3pt shooting. They’re not an intelligent team and play up and down.

What does the math say the biggest upset will be in the first round?

Vickie: New Mexico State over St. Louis is a 13 over 4 and San Diego State over Michigan is a 13 over 4. California over UNLV is a 12 over 5.

John: Any upsets in your Elite 8? No major upsets but I do have 2, 3, and 4 seeds.

Vickie: No major upsets but I do have 1, 2, 3, and 4 seeds.

John: I don’t have any top seeds in my final four because they have been losing lately, but the math is backing up the top seeds.

Vickie: But here’s the real question: will we beat the president?

John: Obama takes the smart, safe approach to the bracket. Historically he has been very good, because he is conservative in his picks and doesn’t bet on upsets. Generally that’s a good way to go. This year is going to be odd since the tops aren’t doing so well. It really could be a 5, 6,or 7 that wins. Nothing crazy based on the math?

Vickie: No, but that doesn’t mean I wouldn’t like to see an upset.

John: Gonzaga has a great RPI, but they’re not ranked high. Their defense metrics must be off . They have a great winning percentage but not necessarily the RPI.

Vickie: But seriously, will we beat the president?

John: He’s playing smart and safe. I want to win, but in an interesting way. It’s a little riskier when you don’t have any #1 seeds in the final 4.

Vickie: Well it’s interesting how similar our brackets are even though we had different strategies! I just got a text from my sister who picked her teams by the color of their uniforms. Blue is her color so she also picks Duke to win this year.

In case you are wondering, the odds of having a perfect bracket are 9.2 Quadrillion to 1. Good luck and have fun.

Check out Tim Chartier’s webinars on the applications of linear algebra for more helpful hints on how to fill out your bracket.

Tim looks at how famous bracketologists have fared in the past (tip — Obama did OK in the 80th percentile, Dwyane Wade, not so much in the 43rd percentile) and provides step by step analysis of the math behind the Colley method and others. He also guides viewers through a free java program that is available for download on his professional web site at Davidson College.

Tim Chartier is an Associate Professor of mathematics at Davidson College. His ability to communicate math both in and beyond the classroom were recognized with the Henry L. Alder Award for Distinguished Teaching by a Beginning College or University Mathematics Faculty Member from the Mathematical Association of America. His research and scholarship were recognized with an Alfred P. Sloan Research Fellowship. Tim serves on the Editorial Board for Math Horizons, a mathematics magazine of the Mathematical Association of America. He also serves as chair of the Advisory Council for the Museum of Mathematics. Tim has been a resource for a variety of media inquiries which includes fielding mathematical questions for the Sports Science program on ESPN. He is co-author with Anne Greenbaum of Numerical Methods: Design, Analysis and Computer Implementation of Algorithms. His latest book, Math Bytes, includes a section on bracketology as well as other fun math and computing endeavors.

In this post for March Mathness, Kenneth Massey whose popular ratings (http://masseyratings.com) help rank the BCS teams each year, offers an overview of what goes into filling out his brackets for March Madness.

Advice on filling out March Madness brackets from Kenneth Massey

I’m a college basketball fan, but to be honest, I don’t watch many games during the regular season. Since my personal expertise is a function of ESPN highlights and commentary, I’ve learned to trust the math more than my own feelings about a matchup.

By following the results, I have a pretty good idea about which teams are over/under rated by the media and which ones are coming on strong or fading into tournament time.

Once the pairings are announced, I usually fill out a bracket based on my limited first-hand knowledge of the teams, the impressions I have from following the rankings, and maybe some “gut” intuitions. For that particular bracket, I don’t do any additional analysis, or even look at the numbers–I just rely on what’s already accumulated in my brain.

Now let me describe how I fill out my more analytical brackets. I have two different strategies, but both of them start with estimating the probabilities that each particular team will advance past each round.
In this post, I will describe that process. In a later post, I’ll describe how I use those probabilities to actually fill out my bracket picks.

I’ve been doing computer ratings for years, and have experimented with many mathematical models, one of which is described in Who’s # 1?. The model I currently use, and post on masseyratings.com, is proprietary, but I will list some of the pertinent aspects of it.

1) Margin of victory matters, but in an intelligent way. There are diminishing returns for blowouts, and adjustments are made for the pace of the game. For example 60-45 may be more impressive than 100-80.

2) Winning is rewarded, especially on the road. Even if the margin is small, a team gets a bump by winning games against good competition.

3) Schedule strength is implicit in all the equations. Everything is measured relative to the opponent, so there is higher reward and less risk for playing tough opponents.

4) The model has a decaying memory of early season games. The team in March is different from the team in November.

5) Games between mis-matched opponents are not as important as games between well-matched opponents. There is a lot more information in a #18 vs #23 matchup than there is when #18 plays #230.

6) My model produces offensive and defensive ratings for each team, as well as homefield advantage estimates. From these, it is possible to predict the distribution of final scores for a hypothetical matchup between any two teams.

After the ratings are computed, I use conditional probability to effectively account for every possible scenario of how the bracket could “play out”. For example, if team X makes it to the Sweet 16, who are they likely to face? According to the seedings, some teams have easier paths of advancement. I can compute the probability that each team advances past a given round, the expected number of rounds a team will win, and ultimately each team’s probability of winning the championship.

The great thing about probabilities is that you are never “wrong”. For example, last year my calculations showed that UConn had an 86% chance of winning the first round, a 54% chance of advancing to Sweet 16, a 29% chance of advancing to Elite 8, 12% chance of advancing to Final 4, 5% of playing in the championship game, and a 2.3% chance of winning it all.

By the nature of randomness, it is not really surprising that underdogs occasionally win. Even a dominant #1 overall seed rarely has more than a 25% chance of winning the entire tournament. That’s what makes the event so exciting–nobody knows what will happen.

After all the probabilities are computed, I proceed to fill in my picks. Don’t I just pick the teams with the highest probabilities? Not exactly. I’ll address that in a subsequent post.